definition square_bishop_set : bishop_set → bishop_set.
intro S; apply (mk_bishop_set (S × S));
-[1: intros (x y); apply ((fst x # fst y) ∨ (snd x # snd y));
+[1: intros (x y); apply ((\fst x # \fst y) ∨ (\snd x # \snd y));
|2: intro x; simplify; intro; cases H (X X); clear H; apply (bs_coreflexive ?? X);
|3: intros 2 (x y); simplify; intro H; cases H (X X); clear H; [left|right] apply (bs_symmetric ??? X);
|4: intros 3 (x y z); simplify; intro H; cases H (X X); clear H;
- [1: cases (bs_cotransitive ??? (fst z) X); [left;left|right;left]assumption;
- |2: cases (bs_cotransitive ??? (snd z) X); [left;right|right;right]assumption;]]
+ [1: cases (bs_cotransitive ??? (\fst z) X); [left;left|right;left]assumption;
+ |2: cases (bs_cotransitive ??? (\snd z) X); [left;right|right;right]assumption;]]
qed.
notation "s 2 \atop \neq" non associative with precedence 90